An Analysis of Abstracted Model-Based Reinforcement Learning

Many methods for Model-based Reinforcement learning (MBRL) provide guarantees for both the accuracy of the Markov decision process (MDP) model they can deliver and the learning efficiency. At the same time, state abstraction techniques allow for a reduction of the size of an MDP while maintaining a bounded loss with respect to the original problem. It may come as a surprise, therefore, that no such guarantees are available when combining both techniques, i.e., where MBRL merely observes abstract states. Our theoretical analysis shows that abstraction can introduce a dependence between samples collected online (e.g., in the real world), which means that most results for MBRL can not be directly extended to this setting. The new results in this work show that concentration inequalities for martingales can be used to overcome this problem and allows for extending the results of algorithms such as R-MAX to the setting with abstraction. Thus producing the first performance guarantees for Abstracted RL: model-based reinforcement learning with an abstracted model.